History of Hindu Mathematics: A Source Book v2.c17.s9.2

v2.c17.s9.2

*Solution.* "Here the number is *x*; multiplied by 200 it becomes 200*x*; added to the square of the number, becomes *x*² + 200*x*; this being multiplied by two, 2*x*² + 400*x*; by this being diminished the fourth power of the number, namely, this *x*⁴, becomes *x*⁴ — 2*x*² — 400*x*. This is equal to a myriad less unity. Equi-clearance having been made, the two sides will be *x*⁴ — 2*x*² — 400*x* = 0*x*⁴ + 0*x*² + 0*x* + 9999. Here on adding four hundred *x* plus unity to the first side, the root can be extracted, but on adding the same to the other side, there will be no root of it. Thus the work (of reduction) does not proceed. Hence here ingenuity (is called for). Here adding to both the sides four times the square of *x*, four hundred *x* and unity and then extracting roots, we get *x*² + 0*x* + 1 = 0*x*² + 2*x* + 100. Again, forming equation with these and proceeding as before, the value of *x* is obtained as 11. In similar instances the value of the unknown must be determined by the ingenuity of the mathematician."¹